Jessica is 2 times as old as Luis. Eighteen years ago, Jessica was 5 times as old as Luis. How old is Luis now?
Answer: We can use the given information to write down two equations that describe the ages of Jessica and Luis. Let Jessica's current age be $j$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $j = 2l$ Eighteen years ago, Jessica was $j - 18$ years old, and Luis was $l - 18$ years old. The information in the second sentence can be expressed in the following equation: $j - 18 = 5(l - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = 2l$ . Substituting this into our second equation, we get: $2l$ $-$ $18 = 5(l - 18)$ which combines the information about $l$ from both of our original equations. Simplifying the right side of this equation, we get: $2 l - 18 = 5 l - 90$ Solving for $l$ , we get: $3 l = 72.$ $l = 24$.